Students will extend their previous understanding of a number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane. The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Big Idea
Students understand and use rational numbers in a way which is meaningful and related to everyday life.
Essential Questions:
How are negative numbers used to represent quantities that are less than zero such as temperatures, scores in games or sports, and loss of income in business?
How is absolute value useful in ordering and graphing positive and negative numbers?
How are positive and negative numbers often used to solve problems in everyday life?
How are rational numbers represented as points on a number line?
How do numbers in ordered pairs indicate locations in quadrants of the coordinate plane?
Vocabulary
Absolute value: The distance between a number and zero on the number line. The symbol for absolute value is shown in the equation |−8| = 8.
Coordinates: An ordered pair, ( x , y ), that locates a point in a plane.
Inequality: Any mathematical sentence that contains the symbols > (greater than), < (less than), < (less than or equal to), or > (greater than or equal to).
Integers: The set of whole numbers and their opposites {... − 3, −2, −1, 0, 1, 2, 3, ... }
Negative numbers: The set of numbers less than zero
Opposite number: Two different numbers that have the same absolute value. Example: 4 and −4 are opposite numbers because both have an absolute value of 4.
Ordered Pair: A pair of numbers, ( x , y ), that indicate the position of a point on the Cartesian Plane.
Origin: The point of intersection of the vertical and horizontal axes of a Cartesian plane. The coordinates of the origin are (0, 0).
Positive number: The set of numbers greater than zero.
Rational number: The set of numbers that can be written in the form a/b where a and b are integers and b ≠ 0.
Sign: a symbol that indicates whether a number is positive or negative. Example: in −4, the (−) sign hows this number is read “negative four”.
x-axis: The horizontal number line on the Cartesian coordinate plane.
x-coordinate: The first number of in ordered pair; the position of a point relative to the vertical axis
y-axis: The vertical number line on the Cartesian coordinate plan.
y-coordinate: The second number in an ordered pair; the position of a point relative to the horizontal axis
Content
understand that positive and negative numbers are used together to describe quantities having opposite directions or values.
understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.
recognize that the opposite of the opposite of a number is the number itself. understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.
recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
find and position integers and other rational numbers on a horizontal or vertical number line diagram.
find and position pairs of integers and other rational numbers on a coordinate plane.
understand ordering and absolute value of rational numbers.
interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
write, interpret, and explain statements of order for rational numbers in real-world contexts.
understand the absolute value of a rational number as its distance from 0 on the number line
interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
distinguish comparisons of absolute value from statements about order.
solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
Understand that positive and negative numbers are used together to describe quantities having opposite
directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits,
positive/negative electric charge); use positive and negative numbers to represent quantities in real-world
contexts, explaining the meaning of 0 in each situation.
6.NS.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
6.NS.6a
Recognize opposite signed of numbers as indicating locations on opposite sides of 0 on the number line; recognize
that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
6.NS.6b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane;
recognize that when two ordered pairs differ only by signs, the location of the points are related by reflections
across one or both axes.
6.NS.6c
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and
position pairs of integers and other rational numbers on a coordinate plane.
6.NS.7
Understand ordering and absolute value of rational numbers.
6.NS.7a
Interpret statements of inequality as statements about the relative position of two numbers on a number line
diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line
oriented from left to right.
6.NS.7b
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write
–3oC > –7oC to express the fact that –3oC is warmer than –7oC.
6.NS.7c
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute
value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account
balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
6.NS.7d
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account
balance less than –30 dollars represents a debt greater than 30 dollars.
6.NS.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
Include use of coordinates and absolute value to find distances between points with the same first coordinate or
the same second coordinate.
Table of Contents
Common Core Learning Standard
Big Idea
Essential Questions:
Vocabulary
Content
Skills Needed
on
Topic
Arc 1: Integers
Direction of Left and Right
- p 517
- Example 2
- p 518 #13-20
WorkbookLearn Zillion: Understand negative numbers using a number line
- p 518 #7-12, 29
Workbook- P525, 526
Learn Zillion: Understanding positive and negative numbers with temperatureLearn Zillion: Understanding positive and negative numbers with money
Learn Zillion: Understanding positive and negative numbers using elevations
Funny video intro to Pos/Neg Numbers
11-1 and 11-4
Learn Zillion: Rewrite Fraction as a Decimal Using Division
Learn Zillion: Understand the opposite of a Number by Using a Number Line
Learn Zillion: Rewrite Decimals as Fractions by Using Equivalent Fractions
Learn Zillion: Understand the Opposite of Decimals by Looking at a Number Line
Learn Zillion: Locate Positive Rational Numbers by Using a Number Line
Learn Zillion: Understand the Opposites by Looking at a Numberline
Use number line as a tool
Give direction (right or left)
- page 520-522
WorkbookLearn Zillion Lessons for 6.NS.7a
11-2
- P511, 524
Rational Numbers Brain PopLearn Zillion Lessons for 6.NS.7b
- p 518 #21-28, 31
- p 519 #37-40, 41
WorkbookXPMath Absolute Value Game
Learn Zillion Lessons for 6.NS.7c
11-1 and CC-12
Learn Zillion Lesson for 6.NS.7d
Arc 2: Coordinate Plane
- p 548-551
Workbook- P515, 526
Homer Simpson Coordinates GameGraph Mole Game
Plotting Points Brain Pop
Plotting Points Math Playground
Learn Zillion Lesson for 6.NS.6b
- p 610-614
Transformations Brain PopLearn Zillion Lessons for 6.NS.6b
11-1, 11-8, and CC-11
- P519-521
Learn Zillion Lessons for 6.NS.6cPlotting Cartoon Characters
Worksheets
11-8 and CC-12
City Blocks
11-8 and CC-12
- P522-523
Learn Zillion Lessons for 6.NS.8Unit Assessments
Standards
directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits,
positive/negative electric charge); use positive and negative numbers to represent quantities in real-world
contexts, explaining the meaning of 0 in each situation.
familiar from previous grades to represent points on the line and in the plane with negative number
coordinates.
that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
recognize that when two ordered pairs differ only by signs, the location of the points are related by reflections
across one or both axes.
position pairs of integers and other rational numbers on a coordinate plane.
diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line
oriented from left to right.
–3oC > –7oC to express the fact that –3oC is warmer than –7oC.
value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account
balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
balance less than –30 dollars represents a debt greater than 30 dollars.
Include use of coordinates and absolute value to find distances between points with the same first coordinate or
the same second coordinate.